In this thesis, I present the results of my research on the X-ray spectra of accreting black holes. The content of this thesis can be broadly separated into two parts: Chapter 2-3 for stellar-mass black holes in X-ray binaries (XRBs) and Chapter 4-6 for supermassive black holes in active galactic nuclei (AGN). This work mainly focuses on the X-ray spectral shape and the spectral variability of these accreting black hole systems. By studying the broad band spectra of XRBs and AGN, we are able to extract some information about the innermost regions of the discs from their X-ray observations. For example, we are able to 1) constrain the size of the coronal region that illuminates the disc; 2) estimate some properties of the discs, such as the density in the disc surface; 3) measure the spin parameters of the accreting black holes. In the meantime, I also study the variability of the innermost regions by comparing different observations or different flux states of individual sources. For example, Chapter 2-3 compare different accretion states of black hole XRBs. Chapter 4 discusses the extreme and fast flux variability on a timescale less than one kilo-second in the narrow-line Seyfert 1 galaxy IRAS 13224−3809. Chapter 5 studies the long-term spectral variability of the Seyfert 1 galaxy 1H0419−577. The main spirit of this thesis is to test for high density discs. A disc reflection model with a variable disc density parameter is used for each source in this work. In the last chapter, I apply the same model to a large sample of Seyfert 1 galaxies in order to compare the disc densities at different black hole mass scales and different accretion rates.